We propose to investigate the possibilities of a new paradigm for nonparametric probability density estimation (NPDE). Recent advances in the fields of NPDE and maximum entropy support the above proposal. It is expected that this new approach to NPDE will be able to unify several ad-hoc procedures currently used in NPDE. This information - theoretic approach to density estimation is defined as a variational problem and uses the Kullback number as the fundamental measure of separation between probability densities. The connections of NPDE with the general problem of smoothing of data, with the estimation of the failure rate in medical experiments and with the problem of pattern recognition in artificial intelligence make the pursuit of a unifying theory of NPDE very desirable.